Finite Group Databasebeta

← #23775548

Subgroups — #23775548

Order 10112.

462 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19099263C211yesmaximal, characteristic, complemented
2#19099198C211yesmaximal, characteristic, complemented
3#19098927C211yesmaximal, characteristic, complemented
4#19098885C211yesmaximal, characteristic, complemented
5#19098880C211yesmaximal, characteristic, complemented
6#19098864C211yesmaximal, characteristic, complemented
7#19098813C211yesmaximal, characteristic, complemented
8#19098796C211yesmaximal, characteristic, complemented
9#19098695C211yesmaximal, characteristic, complemented
10#19098695C211yesmaximal, characteristic, complemented
11#19098673C211yesmaximal, characteristic, complemented
12#19098633C211yesmaximal, characteristic, complemented
13#19098566C211yesmaximal, characteristic, complemented
14#102×D79C211yesmaximal, characteristic, complemented
15#459×C79C211yesmaximal, characteristic, complemented
16C2×D4×D79—21no—
17C2×D4×D79C2211yescharacteristic
18C2×D4×D79C2211yescharacteristic
19C2×#11929609C2211yescharacteristic
20C2×#11929607C2211yescharacteristic, complemented
21C2×C8×D79C2211yescharacteristic, complemented
22#14579154—21no—
23#14579153C2211yescharacteristic, complemented
24#14579144—21no—
25#14579134—21no—
26#14579132—21no—
27#14579132C2211yescharacteristic
28#14579132C2211yescharacteristic
29#14579132C2211yescharacteristic, complemented
30#14579132C2211yescharacteristic, complemented
31#14579129—21no—
32#14579129—21no—
33C4×D316C2211yescharacteristic
34C4×D316C2211yescharacteristic
35C4×C22⋊D79—21no—
36#14579119C2211yescharacteristic, complemented
37C4⋊C4×D79C2211yescharacteristic, complemented
38#14579095C2211yescharacteristic, complemented
39#14579093C2211yescharacteristic, complemented
40#14579092C2211yescharacteristic, complemented
41#14579083C2211yescharacteristic
42#14579083C2211yescharacteristic
43#14579082C2211yescharacteristic, complemented
44#14579082C2211yescharacteristic, complemented
45#14579082C2211yescharacteristic, complemented
46#14579082C2211yescharacteristic, complemented
47#14579082C2211yescharacteristic, complemented
48#14579081C2211yescharacteristic
49(C2×D79)⋊C8C2211yescharacteristic, complemented
50(C2×D79)⋊C8C2211yescharacteristic, complemented
51#14579072C2211yescharacteristic, complemented
52C2×D8×C79C2211yescharacteristic, complemented
53C2×D8×C79C2211yescharacteristic, complemented
54#127×C79C2211yescharacteristic
55C4×D4×C79C2211yescharacteristic, complemented
56C4⋊C8×C79C2211yescharacteristic, complemented
57#102×C79C2211yescharacteristic, complemented
58#102×C79C2211yescharacteristic, complemented
59C23×D79—21no—
60C23×D79—21no—
61C2×D316D411yescharacteristic
62C2×D316C2311yescharacteristic
63C2×C22⋊D79—21no—
64C2×C22⋊D79—21no—
65C2×C22⋊D79—21no—
66C2×C22⋊D79—21no—
67C2×C22⋊D79—21no—
68C2×C22⋊D79—21no—
69D4×D79—22no—
70D4×D79—22no—
71D4×D79—41no—
72D4×D79—41no—
73D4×D79—44no—
74C2×C4×D79—21no—
75C2×C4×D79—21no—
76C2×C4×D79C2311yescharacteristic
77C2×C4×D79C2311yescharacteristic
78#11929609—22no—
79#11929607—41no—
80C2×C79⋊C8C2311yescharacteristic
81C2×C79⋊C8C2311yescharacteristic
82C8×D79—41no—
83C4⋊Dic79D411yescharacteristic
84C4⋊Dic79C2311yescharacteristic
85C4⋊Dic79C2311yescharacteristic
86C4⋊Dic79C2311yescharacteristic
87Dic79⋊C4—21no—
88Dic79⋊C4—21no—
89Dic79⋊C4—21no—
90C22⋊Dic79—21no—
91C22⋊Dic79—21no—
92C22⋊Dic79—21no—
93C22⋊Dic79—21no—
94(C2×D79)⋊C4—21no—
95(C2×D79)⋊C4—21no—
96(C2×D79)⋊C4D411yescharacteristic
97(C2×D79)⋊C4D411yescharacteristic
98C4×Dic79—21no—
99C2×D4×C79—21no—
100C2×D4×C79—21no—
101C2×D4×C79C2311yescharacteristic
102C2×D4×C79C2311yescharacteristic
103C2×D4×C79C2311yescharacteristic
104C22×C4×C79—21no—
105D8×C79—41no—
106D8×C79—41no—
107C2×C8×C79C2311yescharacteristic
108C2×C8×C79C2311yescharacteristic
109C4⋊C4×C79C2311yescharacteristic
110C22⋊C4×C79—21no—
111C42×C79C2311yescharacteristic
112C23×C79—21no—
113C23×C79—21no—
114C23×C79—21no—
115C22×D79—21no—
116C22×D79—42no—
117C22×D79—42no—
118C22×D79—42no—
119C22×D79—42no—
120C22×D79—81no—
121C22×D79—81no—
122C22×D79C2×D411yescharacteristic
123C22×D79C2×D411yescharacteristic
124D4×C79—21no—
125D4×C79—21no—
126D4×C79—21no—
127D4×C79—21no—
128D4×C79—21no—
129D4×C79—21no—
130D4×C79—42no—
131D4×C79—81no—
132C2×C4×C79—21no—
133C2×C4×C79—81no—
134C2×C4×C79C2×D411yescharacteristic
135C2×C4×C79C2×D411yescharacteristic
136C2×C4×C79C2411yescharacteristic
137C22⋊D79—42no—
138C22⋊D79—42no—
139C22⋊D79—42no—
140C22⋊D79—42no—
141C22⋊D79—42no—
142C22⋊D79—81no—
143C2×Dic79—21no—
144C2×Dic79—21no—
145C2×Dic79—21no—
146C2×Dic79C2×D411yescharacteristic
147C2×Dic79C2×D411yescharacteristic
148D316—22no—
149D316—21no—
150D316#4112yes—
151C4×D79—21no—
152C4×D79—21no—
153C4×D79—21no—
154C4×D79—21no—
155C4×D79—42no—
156C4×D79—81no—
157C8×C79—21no—
158C8×C79—21no—
159C79⋊C8—21no—
160C79⋊C8—21no—
161C22×C79—41no—
162C22×C79—41no—
163C22×C79—41no—
164C22×C79—41no—
165C22×C79—41no—
166C22×C79—41no—
167C22×C79—41no—
168C22×C79—41no—
169C22×C79—41no—
170C22×C79C22×D411yescharacteristic
171C2×D79—21no—
172C2×D79—21no—
173C2×D79—22no—
174C2×D79—21no—
175C2×D79—21no—
176C2×D79—21no—
177C2×D79—41no—
178C2×D79—41no—
179C2×D79—84no—
180C2×D79—84no—
181C2×D79AGL(1,ℤ/8)12yes—
182C4×C79—21no—
183C4×C79—21no—
184C4×C79—41no—
185C4×C79C2×#4111yescharacteristic
186C4×C79H(5,𝔽2)11yescharacteristic
187Dic79—21no—
188Dic79—21no—
189Dic79—41no—
190Dic79—41no—
191Dic79—41no—
192C2×C79—81no—
193C2×C79—81no—
194C2×C79—81no—
195C2×C79#54611yescharacteristic
196C2×C79C2×AGL(1,ℤ/8)11yescharacteristic
197C2×C79#57611yescharacteristic
198D79—22no—
199D79—41no—
200D79—42no—
201#3318—791nomaximal, Sylow
202C79#331811yescharacteristic, complemented, Sylow
203#553—791no—
204D42—791no—
205#490—791no—
206#482—791no—
207#481—791no—
208#478—791no—
209#469—791no—
210#466—791no—
211#459D7911yescharacteristic, complemented
212#447—791no—
213#447—791no—
214#442—791no—
215#435—791no—
216#418—791no—
217C2×#102—791no—
218C22×D4—791no—
219C22×D4—791no—
220C22×D4—1581no—
221C2×D8—791no—
222C2×D8C2×D7911yescharacteristic, complemented
223C2×D8C2×D7911yescharacteristic, complemented
224C2×M16—791no—
225C22×C8—791no—
226#127C2×D7911yescharacteristic
227#126—1581no—
228#125—791no—
229#123—1581no—
230#121—791no—
231#121—791no—
232#121—791no—
233#121—791no—
234#121—1581no—
235#121—1581no—
236#120—1581no—
237#120—1581no—
238C4×D4—791no—
239C4×D4—791no—
240C4×D4—1581no—
241C4×D4C2×D7911yescharacteristic, complemented
242#117—791no—
243C2×C4⋊C4—791no—
244#107—791no—
245#106—791no—
246#106—791no—
247C4⋊C8C2×D7911yescharacteristic, complemented
248#102—791no—
249#102—791no—
250#102—791no—
251#102—791no—
252#102—791no—
253#102—791no—
254#102—791no—
255#102—791no—
256#102C2×D7911yescharacteristic, complemented
257#102C2×D7911yescharacteristic, complemented
258C22⋊C8—791no—
259C22⋊C8—791no—
260#97—791no—
261C24—1581no—
262C24—1581no—
263C2×D4—21no—
264C2×D4—21no—
265C2×D4—3164no—
266C2×D4—3161no—
267C2×D4—3161no—
268C2×D4—791no—
269C2×D4—791no—
270C2×D4—1581no—
271C2×D4—1581no—
272C2×D4—1582no—
273C2×D4—1582no—
274C2×D4—1581no—
275C2×D4—1581no—
276C2×D4—1581no—
277C2×D4—1581no—
278C2×D4C22×D7911yescharacteristic
279C2×D4C22×D7911yescharacteristic
280C2×D4C22×D7911yescharacteristic
281C22×C4—21no—
282C22×C4—791no—
283C22×C4—791no—
284C22×C4—1581no—
285C22×C4—1581no—
286D8—41no—
287D8—41no—
288D8—1582no—
289M16—3161no—
290C2×C8—3161no—
291C2×C8—791no—
292C2×C8—791no—
293C2×C8C22×D7911yescharacteristic
294C2×C8C22×D7911yescharacteristic
295C4⋊C4—791no—
296C4⋊C4—791no—
297C4⋊C4—791no—
298C4⋊C4—791no—
299C4⋊C4—1581no—
300C4⋊C4—1581no—
301C4⋊C4—1581no—
302C4⋊C4C22×D7911yescharacteristic
303C22⋊C4—21no—
304C22⋊C4—791no—
305C22⋊C4—791no—
306C22⋊C4—1581no—
307C22⋊C4—1581no—
308C22⋊C4—1581no—
309C22⋊C4—1581no—
310C22⋊C4—1581no—
311C22⋊C4—1581no—
312C42—1581no—
313C42C22×D7911yescharacteristic
314C23—21no—
315C23—21no—
316C23—21no—
317C23—3162no—
318C23—3162no—
319C23—3162no—
320C23—3162no—
321C23—791no—
322C23—791no—
323C23—6321no—
324C23—6321no—
325C23—1581no—
326D4—21no—
327D4—21no—
328D4—21no—
329D4—21no—
330D4—21no—
331D4—21no—
332D4—42no—
333D4—81no—
334D4—3162no—
335D4—3162no—
336D4—3162no—
337D4—3162no—
338D4—3162no—
339D4—792no—
340D4—6321no—
341D4—1582no—
342D4—1581no—
343C2×C4—21no—
344C2×C4—81no—
345C2×C4—3162no—
346C2×C4—791no—
347C2×C4—791no—
348C2×C4—6321no—
349C2×C4—1581no—
350C2×C4—1581no—
351C2×C4—1581no—
352C2×C4—1581no—
353C2×C4—1581no—
354C2×C4—1581no—
355C2×C4—1581no—
356C2×C4D4×D7911yescharacteristic
357C2×C4D4×D7911yescharacteristic
358C2×C4C23×D7911yescharacteristic
359C8—21no—
360C8—21no—
361C8—1581no—
362C8—1581no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22—3161no—
373C22—3161no—
374C22—792no—
375C22—6324no—
376C22—6324no—
377C22—1581no—
378C22—1582no—
379C22—1581no—
380C22—1581no—
381C22—1581no—
382C22—1581no—
383C22C2×D4×D7911yescharacteristic
384C4—21no—
385C4—21no—
386C4—41no—
387C4—3161no—
388C4—3161no—
389C4—3161no—
390C4—1581no—
391C4—1581no—
392C4#41×D7911yescharacteristic
393C4#1457920611yescharacteristic
394C2—81no—
395C2—81no—
396C2—81no—
397C2—3162no—
398C2—3161no—
399C2—1582no—
400C2#1909921011yescharacteristic
401C2AGL(1,ℤ/8)×D7911yescharacteristic
402C2#1909936411yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#459×C79C2
socleC22×C79C22×D4
hypercenter#459D79
hypocenterC79#3318
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #19099263C2semidirect
2. #19099198C2semidirect
3. #19098927C2semidirect
4. #19098885C2semidirect
5. #19098880C2semidirect
6. #19098864C2semidirect
7. #19098813C2semidirect
8. #19098796C2semidirect
9. #19098695C2semidirect
10. #19098695C2semidirect
11. #19098673C2semidirect
12. #19098633C2semidirect
13. #19098566C2semidirect
14. #102×D79C2semidirect
15. #459×C79C2semidirect
20. C2×#11929607C22semidirect
21. C2×C8×D79C22semidirect
23. #14579153C22semidirect
29. #14579132C22semidirect
30. #14579132C22semidirect
36. #14579119C22semidirect
37. C4⋊C4×D79C22semidirect
38. #14579095C22semidirect
39. #14579093C22semidirect
40. #14579092C22semidirect
43. #14579082C22semidirect
44. #14579082C22semidirect
45. #14579082C22semidirect
46. #14579082C22semidirect
47. #14579082C22semidirect
49. (C2×D79)⋊C8C22semidirect
50. (C2×D79)⋊C8C22semidirect
51. #14579072C22semidirect
52. C2×D8×C79C22semidirect
53. C2×D8×C79C22semidirect
55. C4×D4×C79C22semidirect
56. C4⋊C8×C79C22semidirect
57. #102×C79C22semidirect
58. #102×C79C22semidirect
202. C79#3318semidirect
211. #459D79semidirect
222. C2×D8C2×D79semidirect
223. C2×D8C2×D79semidirect
241. C4×D4C2×D79semidirect
247. C4⋊C8C2×D79semidirect
256. #102C2×D79semidirect
257. #102C2×D79semidirect